Mathematics 9709 · AS & A Level · Newton's laws of motion

Newton's laws of motion — practice question

A smooth inclined plane with length $160\text{ cm}$ is set so that one end is $40\text{ cm}$ above the other end, and the lower end lies on horizontal ground. Particles $P$ and $Q$, with masses $0.76\text{ kg}$ and $0.49\text{ kg}$ respectively, are joined by the ends of a light inextensible string that passes over a small smooth pulley fixed at the top of the plane. Particle $P$ is initially held at rest on the same line of greatest slope as the pulley, while $Q$ hangs vertically below the pulley at a height of $30\text{ cm}$ above the ground (see diagram). $P$ is released from rest. It moves up the plane and does not reach the pulley.
(i)[4]

Find the particles’ acceleration and the tension in the string before $Q$ reaches the ground.

(ii)[2]

Find the speed with which $Q$ reaches the ground.

(iii)[3]

Find the total distance travelled by $P$ before it comes to instantaneous rest.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply Newton’s second law to one body so as to form an equation for $a$

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